After the introduction, in the second part of this paper, assigned by “Determination of Problem” we show some peculiarity of mathematics education research within the Stockes’ way on research domain. In the third part following ideas of Anna Sierpinska and Jeremy Kilpatrick, expressed in editorial part of famous book “Mathematics education as a research Domain: A Search for Identity”, we presented five question on research of mathematics education. In the fourth part of this article we survey the history of research on theories in mathematics education. We also briefly examine the origins of this line of inquiry, the contribution of Hans- Georg Steiner, the activities of various international topics groups and current discussions of theories in mathematics education research.